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WXYZ is a trapezoid with mid-segment TR. find the length of TR

User Adi Mor
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Trapezoid have 4 length side lines

Now find proportions

Find height of trapezoid

Divide trapezoid in 1 rectangle and 2 triangles

Then , the 2 triangles have a base of (23-15)/2 = 4

Then height is 4 x WZ x sin 56

Angle Z = (180-56-90) + 90 = 124 degrees

Angle X = 360-124- 56 - 121= 59 degrees

Now look at line 23

Then WZ• cos56 + 15 + XY• cos 59 = 23

Now if both angles Z and Y were similar ,then

TR would be (WX + ZY )/2, because T divides half WZ

BUT theyre not similar, theres a little difference . Then find this difference

Use formula cos (a+b) = cosa• cosb- sina•sinb

then

cos 59 = cos56• cos3 - sin56•sin3

aproximate cos3= 1 , sin3=0

then WZ• cos56 + XY•cos 56 + 15 = 23

(WZ + XY)•(cos56) = 23-15= 8:

(WZ + XY) = 8/(cos56) = 14.285

(WZ + XY)/2 =7.1428

then TZ = 7.1428/2 =3.5714

Finally TR = 15 + 2•TZ cos 56 = 18.994

User MyBoon
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